1 Description
TSIS is an R package for detecting transcript isoform switch for time-series data. Transcript isoform switch occurs when a pair of isoforms reverse the order of expression levels as shown in Figure 1. TSIS characterizes the transcript switch by 1) defining the isoform switch time points for any pair of transcript isoforms within a gene, 2) describing the switch using 5 different features, 3) filtering the results with user’s specifications and 4) visualizing the results using different plots for the user to examine further details of the switches. All the functions are available in the forms of a graphic interface implemented by Shiny App (a web application framework for R) (Chang, et al., 2016), in which users can implement the analysis as easy as mouse click. The tool can also be run just in command lines without graphic interface. This tutorial will cover both in the following sections.
\(iso_i\) and \(iso_j\). The points in the plots represent the samples and the black lines are the average of samples. (A) is the iso-kTSP algorithm for comparisons of two conditions \(c_1\) and \(c_2\). The iso-kTSP is extended to time-series isoform switch (TSIS) in figure (B). The time-series with 6 time points is divided into 4 intervals by the intersection points of average expression. Five features for switch evaluation are determined based on the intervals before and after switch, e.g. the before and after intervals adjoined to switch point \(P_i\).
1.1 Determine switch points
Given that a pair of isoforms \(iso_i\) and \(iso_j\) may have a number of switches in a time-series, we have offered two approaches to search for the switch time points in TSIS:
- The first approach takes the average values of the replicates for each time points for each transcript isoform. Then it searches for the cross points for the average value of two isoforms across the time points (as the example in Figure 1(B)).
- The second approach uses natural spline curves to fit the time-series data for each transcript isoform and find cross points of the fitted curves for each pair of isoforms.
It is reasonable to assume the isoform expression and time-series show curvilinear relationship. However, explicit average values of expression loss precision without having information of backward and forward time points. The spline method fit time-series of expression with control points (depending on spline degree of freedom provided) and weights of several neighbours to obtained designed precision (Hastie and Tibshirani, 1990). The spline method is useful to find global trends of time-series when the data is very noisy. But it may sacrifice the local details of switch. For example, a rough spline fitting with very few control points may results in big shifts of switch points. Users can use both average and spline method to search for the switch points and determine optimal output by looking at the switch plots.
1.2 Define switch scoring features
We define each transcript isoform switch by 1) the switch point \(P_i\) , 2) time points between switch points \(P_{i-1}\) and \(P_i\) as interval before switch \(P_i\) and 3) time points between switch points \(P_i\) and \(P_{i+1}\) as interval after the switch \(P_i\) (see Figure 1(B)). We defined 5 measurements to score each isoform switch. The first two are the probability/frequency of switch and the sum of average sample differences before and after switch, which are similar to Score 1 and Score 2 in iso-kTSP method (Sebestyen, et al., 2015) (see Figure 1(A))). For Score 2, instead of rank differences as in iso-kTSP to avoid possible ties, we directly use the average sample differences.
- Firstly, for a switch point \(P_i\) of two isoforms \(iso_i\) and \(iso_j\) with before interval \(I_1\) and after interval \(I_2\) (see example in Figure1 (B)), Score 1 is defined as
\[S_1 (iso_i,iso_j |I_1,I_2)=|p(iso_i>iso_j |I_1)+p(iso_i<iso_j |I_2)-1|,\]
Where \(p(iso_i>iso_j│I_1 )\) and \(p(iso_i<iso_j│I_2 )\) are the frequencies/probabilities that the samples of one isoform is greater or less than in the other in corresponding intervals. - Secondly, sum of mean differences of samples in intervals \(I_1\) and \(I_2\) are calculated as
\[S_2=d(iso_i,iso_j│I_1 )+d(iso_i,iso_j |I_2)\]
Where \(d(iso_i,iso_j|I_k)\) is the average expression difference in interval \(I_k, k=1,2\) defined as
\[d(iso_i, iso_j|I_k)=\frac{1}{|I_k|}\sum_{m_{I_k}}\left|exp(iso_i|s_{m_{I_k}},I_k)-exp(iso_j|s_{m_{I_k}},I_k)\right|\]
\(|I_k|\) is the number of samples in interval \(I_k\) and \(exp(iso_i|s_{m_{I_k}},I_k)\) is the expression of \(iso_i\) of sample \(s_{m_{I_k}}\) in interval \(I_k\). - Thirdly, a paired t-test is implemented for the two switched isoform sample differences within each interval. The dependency R function for testing is t.test(), i.e.
\[S_3 (iso_i,iso_j |I_k )=pval⇐t.test(x=iso_i \text{ samples in } I_k,y=iso_j \text{ samples in } I_k,\text{paired=TRUE})\]
Where \(k=1,2\) represent the indices of the intervals before and after switch. - Fourthly, the numbers of time points in intervals \(I_1\) and \(I_2\) were also provided, which indicate whether this switch is transient or long lived changes,
\[S_4(iso_i,iso_j|I_k)= \text{time points in interval } I_k\] - Finally, the co-expressed isoform pairs often show good isoform switch patterns of interest. For example highly negative correlated isoforms may present opposite growing patterns along the time frame. As an additional score, we calculated the Pearson correlation of two isoforms across the whole time series
\[S_5 (iso_i,iso_j )=cor(\text{samples of } iso_1,\text{samples of } iso_2 ,\text{method="pearson"})\]
